Solve for q 5/4q=1/3q-2/3+2

$\frac{5}{4} q = \frac{1}{3} q - \frac{2}{3} + 2$

Step 1

Simplify $\frac{5}{4} q$ .

Rewrite.

$0 + 0 + \frac{5}{4} q = \frac{1}{3} q - \frac{2}{3} + 2$

Simplify by adding zeros.

$\frac{5}{4} q = \frac{1}{3} q - \frac{2}{3} + 2$

Combine $\frac{5}{4}$ and $q$ .

$\frac{5 q}{4} = \frac{1}{3} q - \frac{2}{3} + 2$

Step 2

Simplify $\frac{1}{3} q - \frac{2}{3} + 2$ .

Combine $\frac{1}{3}$ and $q$ .

$\frac{5 q}{4} = \frac{q}{3} - \frac{2}{3} + 2$

To write $2$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{5 q}{4} = \frac{q}{3} - \frac{2}{3} + 2 \cdot \frac{3}{3}$

Combine $2$ and $\frac{3}{3}$ .

$\frac{5 q}{4} = \frac{q}{3} - \frac{2}{3} + \frac{2 \cdot 3}{3}$

Combine the numerators over the common denominator.

$\frac{5 q}{4} = \frac{q}{3} + \frac{- 2 + 2 \cdot 3}{3}$

Simplify the numerator.

Multiply $2$ by $3$ .

$\frac{5 q}{4} = \frac{q}{3} + \frac{- 2 + 6}{3}$

Add $- 2$ and $6$ .

$\frac{5 q}{4} = \frac{q}{3} + \frac{4}{3}$

Step 3

Move all terms containing $q$ to the left side of the equation.

Subtract $\frac{q}{3}$ from both sides of the equation.

$\frac{5 q}{4} - \frac{q}{3} = \frac{4}{3}$

To write $\frac{5 q}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{5 q}{4} \cdot \frac{3}{3} - \frac{q}{3} = \frac{4}{3}$

To write $- \frac{q}{3}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{5 q}{4} \cdot \frac{3}{3} - \frac{q}{3} \cdot \frac{4}{4} = \frac{4}{3}$

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{5 q}{4}$ by $\frac{3}{3}$ .

$\frac{5 q \cdot 3}{4 \cdot 3} - \frac{q}{3} \cdot \frac{4}{4} = \frac{4}{3}$

Multiply $4$ by $3$ .

$\frac{5 q \cdot 3}{12} - \frac{q}{3} \cdot \frac{4}{4} = \frac{4}{3}$

Multiply $\frac{q}{3}$ by $\frac{4}{4}$ .

$\frac{5 q \cdot 3}{12} - \frac{q \cdot 4}{3 \cdot 4} = \frac{4}{3}$

Multiply $3$ by $4$ .

$\frac{5 q \cdot 3}{12} - \frac{q \cdot 4}{12} = \frac{4}{3}$

Combine the numerators over the common denominator.

$\frac{5 q \cdot 3 - q \cdot 4}{12} = \frac{4}{3}$

Simplify the numerator.

Factor $q$ out of $5 q \cdot 3 - q \cdot 4$ .

Factor $q$ out of $5 q \cdot 3$ .

$\frac{q (5 \cdot 3) - q \cdot 4}{12} = \frac{4}{3}$

Factor $q$ out of $- q \cdot 4$ .

$\frac{q (5 \cdot 3) + q (- 1 \cdot 4)}{12} = \frac{4}{3}$

Factor $q$ out of $q (5 \cdot 3) + q (- 1 \cdot 4)$ .

$\frac{q (5 \cdot 3 - 1 \cdot 4)}{12} = \frac{4}{3}$

Multiply $5$ by $3$ .

$\frac{q (15 - 1 \cdot 4)}{12} = \frac{4}{3}$

Multiply $- 1$ by $4$ .

$\frac{q (15 - 4)}{12} = \frac{4}{3}$

Subtract $4$ from $15$ .

$\frac{q \cdot 11}{12} = \frac{4}{3}$

Move $11$ to the left of $q$ .

$\frac{11 q}{12} = \frac{4}{3}$

Step 4

Multiply both sides of the equation by $\frac{12}{11}$ .

$\frac{12}{11} \cdot \frac{11 q}{12} = \frac{12}{11} \cdot \frac{4}{3}$

Step 5

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{12}{11} \cdot \frac{11 q}{12}$ .

Cancel the common factor of $12$ .

Cancel the common factor.

$\frac{12}{11} \cdot \frac{11 q}{12} = \frac{12}{11} \cdot \frac{4}{3}$

Rewrite the expression.

$\frac{1}{11} (11 q) = \frac{12}{11} \cdot \frac{4}{3}$

Cancel the common factor of $11$ .

Factor $11$ out of $11 q$ .

$\frac{1}{11} (11 (q)) = \frac{12}{11} \cdot \frac{4}{3}$

Cancel the common factor.

$\frac{1}{11} (11 q) = \frac{12}{11} \cdot \frac{4}{3}$

Rewrite the expression.

$q = \frac{12}{11} \cdot \frac{4}{3}$

Simplify the right side.

Simplify $\frac{12}{11} \cdot \frac{4}{3}$ .

Cancel the common factor of $3$ .

Factor $3$ out of $12$ .

$q = \frac{3 (4)}{11} \cdot \frac{4}{3}$

Cancel the common factor.

$q = \frac{3 \cdot 4}{11} \cdot \frac{4}{3}$

Rewrite the expression.

$q = \frac{4}{11} \cdot 4$

Combine $\frac{4}{11}$ and $4$ .

$q = \frac{4 \cdot 4}{11}$

Multiply $4$ by $4$ .

$q = \frac{16}{11}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$q = \frac{16}{11}$

Decimal Form:

$q = 1.\overline{45}$

Mixed Number Form:

$q = 1 \frac{5}{11}$

Solve for q 5/4q=1/3q-2/3+2

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